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Simplifying n2 + -8n + -72 = 0 Reorder the terms: -72 + -8n + n2 = 0 Solving -72 + -8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -8n + 72 + n2 = 0 + 72 Reorder the terms: -72 + 72 + -8n + n2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -8n + n2 = 0 + 72 -8n + n2 = 0 + 72 Combine like terms: 0 + 72 = 72 -8n + n2 = 72 The n term is -8n. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8n + 16 + n2 = 72 + 16 Reorder the terms: 16 + -8n + n2 = 72 + 16 Combine like terms: 72 + 16 = 88 16 + -8n + n2 = 88 Factor a perfect square on the left side: (n + -4)(n + -4) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (n + -4) equal to 9.38083152 and -9.38083152.Subproblem 1
n + -4 = 9.38083152 Simplifying n + -4 = 9.38083152 Reorder the terms: -4 + n = 9.38083152 Solving -4 + n = 9.38083152 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = 9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + n = 9.38083152 + 4 n = 9.38083152 + 4 Combine like terms: 9.38083152 + 4 = 13.38083152 n = 13.38083152 Simplifying n = 13.38083152Subproblem 2
n + -4 = -9.38083152 Simplifying n + -4 = -9.38083152 Reorder the terms: -4 + n = -9.38083152 Solving -4 + n = -9.38083152 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = -9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + n = -9.38083152 + 4 n = -9.38083152 + 4 Combine like terms: -9.38083152 + 4 = -5.38083152 n = -5.38083152 Simplifying n = -5.38083152Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.38083152, -5.38083152}
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